Vague Objects

Allow me to introduce my cat, Pinky.

Pinky the Cat

My cat, Pinky, has one semi-detached hair.

The metaphysical question at hand is this: Is the semi-detached hair a part of Pinky or not?

Any way you slice it, there’s some vagueness here. The more usual thought in philosophy is that the world is perfectly unvague — the world is utterly precise (the loose hair either does or does not belong to Pinky), everything just is whatever it is, and whatever vagueness humans encounter is simply a matter of human imprecision. Either our knowledge-generating faculties or our language faculties (or both, if there’s a difference), are imperfect, and incapable of discovering/representing the perfection of the world.

But there’s another possibility: The world itself is a vague place, and, even if we had perfect knowledge-generating faculties, we’d still struggle with issues of vagueness, because those issues are embedded in the fabric of nature.

So, let’s agree that there is indeed some vagueness at play, and ask: Is this vagueness actually in the world, or is it in our language/thoughts about an unvague world?

Unvague Cats; Vague Language/Thought

If the vagueness is just in our language, and not in the world, then there is a fact of the matter as to whether or not Pinky has that loose hair as a part of itself. If Pinky does indeed own that hair, then “Pinky” picks out the cat-like mass along with the loose hair.

Which cat is Pinky?

Which cat is Pinky? The one with the loose hair, or the one without?

As Michael Morreau sees it, this actually generates a metaphysical problem:

If vagueness is all a matter of representation, there is no vague cat. There are just the many precise cat candidates that differ around the edges by the odd whisker or hair. Since there is a cat,… and since orthodoxy leaves nothing else for her to be, one of these cat candidates must then be a cat. But if any is a cat, then also the next one must be a cat; so small are the differences between them. So all the cat candidates must be cats. The levelheaded idea that vagueness is a matter of representation seems to entail that wherever there is a cat, there are a thousand and one of them, all prowling about in lockstep or curled up together on the mat. That is absurd. Cats and other ordinary things sometimes come and go one at a time.

Pinky and Blinky

Pinky and Blinky: Two different cats that share the same (mostly) space.

If the world is not vague, then both of these are perfectly unvague cat objects, and if one is a cat then there’s every reason to say that they both are. In fact there are thousands (billions? trillions?) of cats here, all walking around in one lump. So on the world-is-not-vague side, we have the repercussion of “Pinky” picking out one specific cat out of many taking up mostly the same space; Winky, Glinky, Zinky, Inky, Kinky, etc.

Vague Cats

So, let’s try the world-is-vague approach instead. On the world-is-vague side, there’s just one cat, but that cat is itself vague. There’s no metaphysical fact of the matter as to whether or not that loose hair counts as a part of Pinky. But that loose hair doesn’t suddenly create two unvague cats: Pinky and Blinky.

What would be problematic about a vague world like this?

Perhaps the biggest problem would be representational. If Pinky is a vague cat, then we have no chance of ever compiling the perfect representation of him. (The perfect representation would include a representation of that loose hair, if it’s a part of Pinky; and it would not include that hair if it’s not a part of Pinky. But if it’s vaguely attached to Pinky, our representations will fail in one direction or the other.) Those prone to thinking that representations should strive for perfection will be most unhappy with this state of affairs.

A related problem crops up in the philosophy of language. Language philosophers like to think that names (like “Pinky”) pick out unique, unvague objects (like Pinky). But if Pinky is himself vague, then the name “Pinky” can’t unambiguously refer to Pinky. This is particularly problematic for anyone harboring vestiges of a description theory — if that loose hair may or may not belong to Pinky, then we have a problem coming up with a complete description, wherein that hair plays a part (or not).

What would be the payoff for accepting vague cats into our ontologies? The non-proliferation of tightly bound brother cats to Pinky, for one thing. (There is no need, if Pinky is vague, to posit the existence of Blinky, Winky, Glinky, et al, existing in nearly the same space as Pinky.)

It also buys us a platform to talk intelligibly about such metaphysical conundrums as the Sorites paradox. If, similar to cats, heaps are vague, as opposed to just our knowledge of heaps being vague, we can escape some of the problems inherent with talking about heaps changing over time.

We’ll be talking about the Sorites paradox in a future post.

For now, take some comfort in the idea that your knowledge of the world isn’t inherently imperfect. The world itself is inherently imperfect.

Of course, knowing that might make you uncomfortable again. Sorry.


Morreau, Michael. “What Vague Objects Are Like,” Journal of Philosophy 99, 2002.

Science and What Exists

To make the transition to Einstein’s universe, the whole conceptual web whose strands are space, time, matter, force, and so on, had to be shifted and laid down again on nature whole.

—Thomas Kuhn

One problem metaphysicians have been dealing with for, well, forever, is the unfortunately necessary intertwining of metaphysics and epistemology. Metaphysics is the philosophical study of what exists; epistemology is the philosophical study of knowledge. And it’s trivial to point out that the best we can do in detailing what there is that exists is to rely on our best epistemology: We can’t talk about what we know about, without talking about what (and how) we know. If we know about quarks, it’s not simply the case that quarks exist, but that we figured out that they exist. Our catalogue of items in the universe is inherently tied to our knowledge of those items.

Why is this problematic? Well, many metaphysicians are very conscious and conscientious about keeping existence separate from knowledge of existence. Much of the problem can be traced back to the venerable Bishop Berkeley, who posited that everything in the universe in actually mind-dependent for its very existence — it’s not, Berkeley thought, just that the computer screen in front of you is merely hidden from view when you close your eyes, but that this lack of observation actually means the computer screen is not really there when your eyes are closed. Problems with this theory forced Berkeley to say that God observes everything at all times, and so there’s no worry about things blinking in and out of existence with the blink of an eye. God never blinks. But regardless of the absurdity of this centuries-old bit of philosophy, the aftershocks have stayed with us. There’s something very compelling, apparently, about the idea that our minds have metaphysical power — that minds can create some of reality.

The great irony is that the best scientifically-minded philosophers of the 20th Century, while trying to shore up the mind-independence of the external world, actually gave proponents of mind-dependence a strong foothold in the metaphysical debate.

Naturalized epistemology — the brain child of W.V.O. Quine, though it was clearly anticipated hundreds of years earlier by David Hume — takes science to be the paragon of knowledge-farming; the discipline whose results we are most certain about. Naturalism, though, if we accept it, forces us also to acknowledge the following: We can’t make judgements about the world from some point of privileged access outside of science. That is, there is no way to step outside science and see what there is in the world; we don’t get a clearer picture of quarks without science — science itself tells us about quarks, and without science this piece of ontological furniture would not be accessible to us whatsoever. Our metaphysical house, chock full of interesting furniture, wouldn’t merely look somewhat different without science; it would be a bare, dirt-floored cabin with very little of interest in it.

This leads to a very tantalizing point. Science often changes its mind, and in such episodes of change what we take to be our ontology (our catalogue of things that exist) changes as well. For instance, once upon a time science told us that there was a substance called phlogiston that is released from things when they are burned. This substance — a consequence of a good scientific theory that explained several phenomena related to chemistry — was taken by scientists (and the informed public) as existing in the world. If science is our best arbiter of what exists, then, at the time during which science told us that phlogiston existed, there’s a strong sense in which it actually existed. Science, remember, tells us what there is, and there’s not privileged perspective outside of science to figure out our metaphysics. It turned out, however, that the phlogiston theory of chemistry ran into serious problems, and was more or less wholesale replaced by the oxygen theory of Lavoisier. In this new theory, there was no place for phlogiston. At this point, science told us that phlogiston does not exist.

There are (at least) two conclusions that can be drawn from this, each of which I will encapsulate using the Kuhnian metaphor at the top of this entry:

Standard Naturalism: The whole of science forms a conceptual web from which vantage point we purvey the world. There is no spot outside of the web from which to purvey the world. We can change science by changing some part of the web — this amounts to changing our ideas about an unchanging world. The world is independent of our ideas about it, even as we discover new ways to look at what exactly is in it. For instance, we were simply wrong about the existence of phlogiston. It never existed.

Kuhnian Mutant Naturalism: A scientific theory is a conceptual web that uniquely lays upon the world giving it its shape. When a new theory is developed, an entirely new web is made. There is still no place outside of the web from which to purvey the world, but we can shuck off the entire web in favor of a new one. The world is partly dependent for its existence on our ideas about it — whichever web we throw onto the world actually gives the world its shape. When we change our ideas, we change the world. For instance, phlogiston actually did exist while scientists were working with phlogiston theory. When Lavoisier came up with a new chemical theory, the world actually changed — phlogiston disappeared, and in its place oxygen and other items filled our metaphysical cupboards.

Many have noted from Kuhn’s version of naturalism that he is an anti-realist in the Kantian vein. We won’t get into the thickets of Kantian metaphysics here, but, in short, he believes that our ideas are not merely a pre-condition for theorizing about things, but that theorizing indeed is a pre-condition for the very existence of things. Contrary to this, standard naturalism usually goes hand in hand with common-sense and scientific realism, wherein, as Philip Kitcher notes: “Trivially, there are just the entities there are. When we succeed in talking about anything at all, these entities are the things we talk about, even though our ways of talking about them may be radically different.”

One reason Kuhn is led to his odd metaphysics is because of his implicit description theory of reference. On a description theory, the only way to correctly refer to an entity is to have its unique description in mind; but if a scientific revolution changes the description associated with a key scientific term, then the old description no longer refers. This leads Kuhn to the idea that competing scientific paradigms are incommensurable. It also motivates his metaphysics. If a term once referred and now it does not, all on the basis of our changing descriptions, then by some inferential jump one could think that this correlation was causal; i.e., that our changing descriptive thoughts cause a change in the world.

We’ll examine description theories and the philosophy of language in an upcoming post. Stay tuned…

Do Numbers Exist?

According to your disposition, you might have an immediate gut reaction to this question. My initial reaction (oh so long ago) was: “Of course numbers don’t exist. You can’t pick up the number 3 and throw it through a window.” That is, my intuition was that the only things that exist are the kinds of things that can be physically manipulated, and numbers, by almost every account, just aren’t this kind of thing.

To be clear about our terms, you can pick up numerals — that is, you can pick up concrete instances of numbers, like the plastic number signs at the gas station telling you how much gas costs, or the printed numerals in a book, denoting page numbers. But you don’t, by virtue of tearing out page three of a book and tossing it out a window, throw the number 3 out the window, any more than you throw me out of a window by drawing a picture of me and throwing that out the window.

Numbers, if they exist, are generally what philosophers call abstract objects, and those who maintain that such things exist claim that they exist outside of space and time. If you’re like me, you shake your head at such talk. “Outside of space and time? What does that even mean? Gibberish!” If you are similarly disposed, you might be a nominalist (in case you’re accumulating self-descriptive philosophical terms), and you are part of a long, proud philosophical tradition that thinks that existence is the exclusive domain of the physical.

However, your nominalism begins to run into problems pretty quickly. Never mind numbers. What about things like, say, novels? What exactly is the novel The Catcher in the Rye? It’s not any of the particular instantiations of it — it’s not the copy on your bookshelf; it’s not the copy on mine. All of the print copies on the planet could be eradicated and still the novel could be able to be said to exist. Is the novel the original manuscript sitting in a safe somewhere? But that could be burned and you could still argue that the novel exists. But if the novel itself is not identified with any of its particular instantiations, then the nominalist is in a bit of a quandary. On this perspective, the copies of the novel are instantiations of the novel itself, and the novel itself is seeming to be something abstract — something non-physical.

So the idea of something somehow existing outside space and time is suddenly not as absurd as it may have seemed. What about numbers, then? Of course there are disanalogies between numbers and novels. Novels are invented by humans, while, on most views of the subject, numbers exist whether or not humans ever happened to discover them. But, putting such differences aside for the moment, perhaps the existence of novels as abstract objects gives us some traction to say that numbers exist as abstract objects.

Abstract objects

What other sorts of things could be included in the category of abstract objects? The funny thing is that in many seminal texts on the subject, one has to plumb deep to find mention of what would count as an abstract object. Mathematical objects generally top the list (numbers, points, lines, triangles, etc.), followed by things like chess moves, games in general, pieces of music, and propositions. How are these things abstract? We generally think of a chess move, for instance, as something that exists by virtue of a concrete chess player actually moving a concrete chess piece in accordance with the rules of the game (which could themselves be considered abstract, but never mind this for the moment). But that seemingly concrete move can be instantiated in so many concrete ways — you could be replicating someone else’s game on your own chess board, you could make the move on a hundred different boards all at (nearly) the same time, you could make the move in your head before you make it on the board,… and all of these concrete possibilities point to the metaphysical problem here: If you believe there is only one move, and it’s concrete, then which move is the one move? And then what are the other moves? Copies of the move? Or instantiations of the same move? If you believe in abstract objects, you have, on some takes, an easier time of it. The move itself is an abstract object, and every physical version of that move is a concrete instantiation of that move. That is, none of the concrete, physical moves are actually the move — there is only one move and it is abstract, and any physical move is a copy, like a sculpture of a real person. (You can have a thousand sculptures of a person, but there’s only one person. The sculptures are imitations or instantiations of the person.)

This perspective is (loosely) called platonism, named after Plato’s idea that there are ideal “forms” — perfect archetypes of which objects in the real world are imperfect copies.

Why would these ideal forms not exist in space-time? I.e., why would they have to be abstract? Well, objects in space-time (the real world) are all imperfect copies of something. So if an ideal form existed in, say, your living room, then it would be non-ideal by virtue of existing in your living room. To put it perhaps less question-beggingly, if, say a chess move were instantiated in a thousand ways, how would you pick out the ideal version from which all others were copied? All of the instantiations would have similar properties, and so no one instantiation would stand out as different enough to count as the move, the platonic form of that move. Therefore, it makes sense to posit an abstract version of the move — something perfect, and outside of space-time, from which all the worldly versions are copied.

Thinking about geometric objects is perhaps the clearest way to think about abstract objects. A line segment (a true, geometric line segment) is a perfectly straight, one-dimensional object with a determinate length. There are no such objects in space-time. Every object you could possibly interact with is three-dimensional — no matter how thin a piece of, say, plastic you create, it always has a height and a thickness, giving it three dimensions. Nothing, therefore, in the concrete world, is a real geometric line segment. We have things that approximate line segments — very straight, very thin objects. But none of those things will ever be perfectly straight and with zero thickness. So if there does, somehow, exist a true line segment, it certainly isn’t in the concrete world, and therefore it must be in some sort of abstract realm.

Knowledge of abstract objects

One of the most damning aspects of platonism is its failure to come to terms with how we learn things about abstract objects. The general picture of how we acquire knowledge goes something like this: We perceive an object in the physical world, via physical means (e.g., light bounces off the physical object and hits our eyes), and eventually we process such perceptions in our brains and work with mental representations — i.e., brain states — of the object in question. But an abstract object can’t be processed like this. It is non-physical, and so, e.g., light can’t reflect off of it. So our usual causal theory of knowledge acquisition fails for things like numbers.

Well, then, how is it that we come across any knowledge of abstract objects, if they indeed exist? Some mathematical platonists, like the venerable logician Kurt Gödel, resorted to the idea that we just know truths about mathematical abstracta. As he wrote:

But, despite their remoteness from sense experience, we do have a perception also of the objects of set theory, as is seen from the fact that the axioms force themselves upon us as being true. I don’t see why we should have less confidence in this kind of perception, i.e., in mathematical intuition, than in sense perception…

But this is clearly an unacceptable answer to the problem of knowledge of abstract objects. How exactly do the axioms of set theory force themselves upon us? Waving your hands and saying “they just do” isn’t an account of the process, and leaves us in the dark as to how they just do, which is precisely what we need before we can take the platonist seriously as an epistemologist. (One need merely look at the history of geometry to see one serious problem with seeing the “obvious” truth of axioms. Until Lobachevsky and Riemann came along with consistent non-Euclidean geometries, nearly everyone though that Euclid’s fifth postulate “forced itself upon us”.) How does some feature of a non-spatiotemporal object force itself upon our spatiotemporal brains? The only way would be somewhat magical, and you could look to Descartes to see the folly of such a plan. Descartes posited that minds are distinct substances from brains, and indeed were non-spatiotemporally located. Of course, this leaves the problem of how the mind somehow slips into the brain and affects it. Descartes’ answer was that it crept in through the pineal gland. But this is no answer; it merely delays the answer for a moment. How does the non-spatiotemporal mind creep in through the pineal gland, and then into the brain? Descartes had no answer for this, of course, because the whole thing would be terribly mysterious, explaining how the non-physical interacts with the physical.

Worries like this keep nominalists well-motivated to stay on their side of the debate.

The argument from indispensability

Even if you’re dead-set against granting the existence of numbers, you think platonism is absurd, you have challenged platonism’s picture of knowledge, and you somehow have all of your nominalist ducks in a row, there is still one very influential argument to contend with as regards numbers’ existence: The argument from indispensability. Hardcore nominalists are often quite scientifically-minded, scientifically-motivated philosophers. And it is this love of science that gets them into trouble with denying the existence of numbers. The argument runs, in broad strokes, like this:

  1. Science is the best arbiter of what exists.
  2. Therefore, if science says something exists, we should accept it.
  3. Science relies (heavily and intractably) on mathematics.
  4. Therefore, science says that numbers exist.
  5. Therefore, numbers exist.

If you’re a good nominalist, you’re more than likely feeling obliged to accept this argument as sound. But if you accept its conclusion, then you’re right back to the issue of explaining what numbers are. They can’t be physical objects, therefore they must be abstract. But, as a nominalist you claim that there are no abstract objects! And you are caught in an intractable dilemma.

Many nominalists give up at this point. Hilary Putnam wrote resignedly:

Quantification over mathematical entities is indispensable for science…; but this commits us to accepting the existence of the mathematical entities in question. This type of argument stems, of course, from Quine, who has for years stressed both the indispensability of quantification over mathematical entities and the intellectual dishonesty of denying the existence of what one daily presupposes.

The talk of “quantification” is a bit of logic talk, but we can paraphrase it into regular English: “If science uses numbers, then science is committed to the existence of numbers.” You might see a glimmer of nominalist hope here. Science also uses frictionless planes, for example, and yet no scientist feels committed to the existence of those. Perhaps there is a way out of our commitment to numbers in the same way. Or perhaps, one might argue, frictionless planes actually do exist as platonic, abstract objects.

But there are two more “obvious” ways to be a nominalist about mathematics.

First, you could argue that numbers exist, and are actually physical objects. Penelope Maddy argues something close to this in her early work, Realism in Mathematics. She actually is here arguing for a version of naturalized platonism — the idea being that what is usually thought of as abstract objects are actually somehow existent in the physical world. But, platonist labels aside, the gain for nominalism on this take would be obvious: numbers, if they are physical objects, would be just another part of the down-to-earth nominalist physical world, like cats, trees, and quarks. This brave strategy, however, ultimately fails. It would take us into some metaphysical thickets to explain why, so I have relegated this to a paragraph at the very end of this post.

Second, you could argue that numbers aren’t actually indispensable to science. Hartry Field famously tried this strategy, claiming that science in fact only seems to rely on mathematics. On Field’s view, this seeming reliance is really just a fiction. In order to prove this Field attempted to nominalize a chunk of physics, by removing all reference to numbers within it. This complicated, counterintuitive project has met with equal parts awe and criticism. The consensus is that his project is untenable in the long term.

So do numbers exist or not?

Well, if you’re a platonist, you would answer “yes, numbers exist”. And further you would claim that they possess a sort of existence that is abstract — different from the sort of existence that stones, trees, and quarks enjoy. Of course, this means you are in the unenviable position of explaining the coherence of this sort of existence, along with the herculean task of explaining how we know about anything in this abstract, non-physical realm.

If you’re a nominalist, you’d probably answer “no, numbers do not exist”. However, now you have the unenviable job of explaining why mathematics seems so indispensable to science, while science is perhaps our best tool for saying which things exist. The two best nominalist answers to this conundrum seem untenable.

Probably, as is usually the case in philosophy, dogmatically sticking to one side of a two-sided debate will be inadequate. Maddy’s attempt at naturalizing platonism was a brave bridge across the nominalist-platonist divide, but clearly isn’t the right bridge. We’ll examine some other options in a future post.

References and Further Reading

Balaguer, Mark. (1998) Platonism and Anti-platonism in Mathematics. Oxford: Oxford University Press.

Benacerraf, Paul. (1973) “Mathematical Truth”, Journal of Philosophy 70.

Colyvan, Mark. (2001) The Indispensability of Mathematics. Oxford: Oxford University Press.

Irvine, A.D. (1990) Editor. Physicalism in Mathematics. Dordrecht: Kluwer.

Lowe, E. & Zalta, E. (1995) “Naturalized Platonism Versus Platonized Naturalism,” Journal of Philosophy 92.

Maddy, Penelope. (1992) Realism in Mathematics. Oxford: Clarendon Press. Revised paperback edition.

A note on Maddy’s naturalized platonism

Maddy actually thinks that we perceive sets. Number theory, as many logicians are proud to point out, can be reduced to set theory — i.e., numbers can be reduced to sets, which are, of course, generally seen as just another sort of abstract object. Maddy’s move is to bring those sets into the natural world. So that when we see an egg, we are perceiving that egg, but are also perceiving the set containing that egg. (A set containing an object is different from the object itself, you may recall from your math studies.) And that set containing the egg is a natural object, different from the egg itself. But now we run into trouble. Certainly there must be something different between an egg and a set containing that egg; otherwise ‘set containing that egg’ is just a proper name denoting the egg in question, and nothing metaphysical hangs on the distinction. (If you call me “Alec” or “author of this post”, you are not positing the existence of two people — these are just two different names for the same person.) Well, the usual distinguishing feature of abstracta is that they are not spatiotemporally located; but on Maddy’s scheme sets are spatial objects. The problem: Our egg and the set containing it necessarily co-exist in the same exact region of space-time, and yet they are supposed to be different things. In what does this difference consist? Well, certainly nothing physical, otherwise they wouldn’t co-exist in the exact same region of space-time. But then the difference must be something non-physical — i.e., something about the set must be abstract. And if this is the case, then we’re right back to all of the problems inherent in platonism, particularly the problem of how we can have any knowledge of such abstracta.

What is True Depends on What is the Truth

This is a follow-up to Alec’s nicely written post on realism and its varieties. I put forth in the comments section the idea that what one believes to be the case with regards to realism v. anti-realism is going to color what one takes to be true in the world. Or, at the very least, what one considers to be a candidate of truth in the world. Here is why that is (and note that this is not merely my opinion, but is an established line of argument and belief among metaphysicians).

Realism, as Alec eloquently stated, is the view that the world is a particular way in a mind-independent fashion. Anti-realism is the view that the world is mind-dependent, and so derives many, perhaps all, of its features because of how it is perceived. Those are very quick takes on the two views and should not be satisfactory in and of themselves to anyone. Again, I refer you to Alec’s post.

Depending on which of the views you hold, your idea of what is true (or at least what you believe to be true) need not change, but what makes something true (its truth conditions) does change. Why might this be? First, let’s talk about the common sense view of truth.

Suppose a person makes the following utterance, “snow is white.” That utterance has a truth value. It is true if snow is white, and it is false if snow is any color other than white. How do we go about determining if it is true? Well, we go and look at snow. “Look”, you might say, if you live somewhere other than NYC or Chicago, “there is some snow, and it is white.” Hurray! We have verified its truth status. Or, dum dum dum, have we?

If you are a realist, you think that there are properties in the world that we can discover. This does not just mean that we can encounter snow, but that when we encounter snow, we can learn something about it, such as it being cold, malleable, crunchy, and white. If those are characteristics that we cannot discover or encounter, there is no way we can determine the truth value of any statements that make reference to such characteristics. The utterance, “snow is white”, is true only if snow is actually white. We laugh at a child who says, “snow is brown” because we know that snow is not brown (even in NYC, snow is white until it hits the dirty, dirty ground there). This is called the correspondence theory of truth. An utterance is true if it corresponds with what is actually the case in reality. “My keys are in the bowl by the door” is only true if my keys are in the bowl that is by the door. If they are in a dish, if they are in the kitchen, if I have no keys at all, the utterance is false because it does not correspond with how things actually are in reality. Hopefully you can see why a realist is drawn to the correspondence theory (though the two are not necessarily conjoined).

But I suspect you can also see why the anti-realist is not going to favor a correspondence theory of truth. For the anti-realist, most of what we believe to be the case about the world is due to how our minds project or create certain features or characteristics of what we perceive. For the anti-realist, the utterance of “snow is white” is expressing an opinion since there is no objective characteristic of ‘white’ in the world; there is only the experience that I refer to as ‘being white’. Whiteness, then, is a mind-dependent characteristic. It exists only because our minds create it. What does that do to the truth value of the utterance then? Well, as there is no objective reality to compare the utterance to, we cannot rely on the correspondence theory. Even if there were an actual characteristic of being white in the world, how could we ever know what that characteristic was like when our perceptions are so unreliable? And yet, the anti-realist does not want to say that there is no such thing as truth. Instead, what determines truth is something different from correspondence. It is called the coherence theory of truth. For the anti-realist (for many of them, at least), our mind-dependent experiences build up a large collection of beliefs about what we think the world is like. Since we cannot say what the world is actually like, we judge truth based on how well an utterance coheres (fits in) with our collection of beliefs. We want our collection of beliefs to be as coherent as possible. Note that coherence here does not merely mean understandable or rational, it means something larger: that our collection of beliefs not contain contradictions. We do not want to believe that we are both standing in the rain and we are not standing in the rain. We do not want to believe that snow is white together with snow is not white. (Of course, we can believe variations of those, but the contradictions are smoothed away by adding unspoken caveats to the utterance. For example, “snow is white” need not contradict “snow is not white” if we have the unspoken belief that the second utterance is about NYC snow which is changed or altered snow. “I am standing the rain” need not contradict “I am not standing in the rain” so long as we have the unspoken belief that I am standing beneath an umbrella which means that I am in the rain without being rained upon.)

Truth and Language
This can quickly become an issue of semantics or philosophy of language and so worth another, different post. Briefly, though, we know what we mean when we say what we do. When I point at snow and say, “snow is brown”, I do not literally mean that I believe snow is brown. Instead, I mean that snow, in such and such a state or condition (whatever condition is present, perhaps), is brown. If someone, maybe Alec, who knows, were to ask me, “do you mean to say that you think snow is brown?” I can honestly and reasonably say, “That is not what I meant when I said, ‘snow is brown.’ I meant that the snow here is brown, by which I meant to say, this is some really dirty snow.’” There is the demonstratrive sense of the utterance, by which I point and so indicate a particular batch of snow. Think of the old example about eskimos having eighteen different words for snow. That is a ridiculous example, I think, meant to suggest that eskimos like snow so much they talk about it a lot. But guess what? We non-eskimos have lots of different words for snow too: snow, wet snow, dry snow, soft snow, heavy snow, light snow, sleet, hail, etc. Wait a minute, you might exclaim, those are just the word ‘snow’ with an adjective in front of it. Yep — many of our words are like that. In fact, many words are like that: compound concepts captured in one word. What does ‘slush’ mean, if not icy rain? What is ‘beautiful’ aside from ‘pretty’ preceded by some number of ‘very’s?

Back to the topics at hand though, for an utterance to be true for the anti-realist, then, just means that the utterance fits in with my already accepted beliefs. “Snow is white” is true if what I call ‘snow’ is associated with the characteristic that I call ‘white’, and it means nothing beyond that. So, which theory of truth is correct? The realist theory is not correct, as there is no way to verify if what we have said actually corresponds with what is actually the case in the world. There is the experience I have whenever I come across a sensation that I label ‘white’, but why think that particular experience matches up with the way the world truly is? Perhaps I am color blind. Perhaps I am hallucinating. But you are not, the realist might contend. But how do you know that I am not? Can you prove that you are sensing the world as it actually is? If you could, there would be no anti-realist camp.

The anti-realist theory is not true either though, at least not obviously so. Coherence is an important attribute for any system of beliefs. For any system of beliefs, we want there to be as few outright contradictions as possible. Yet, why think that coherence alone is enough to establish truth? Someone who is schizophrenic or just simply insane might have a very coherent view of their experiences, but it only seems coherent to them because they are crazy. The schizophrenic person believes he hears voices separate from his own; he may even believe he sees people talking to him. We consider him sick though, because he is experiencing what no one else is or can. We say that the schizophrenic is wrong, not because his beliefs are not coherent, since many of them are (perhaps even as many of his beliefs cohere as do our own), but because he has beliefs that do not correspond to reality, to what we think is actually true. A claim, by the way, the schizophrenic will agree with once he is on successful medication.

What is the upshot of all this? Well, the realist maintains that our intuitive conception of truth is based on correspondence, not coherence, and the anti-realist maintains that we can never know whether our beliefs correspond with anything external to the mind, but that we can determine if our beliefs cohere with one another. Which you favor seemingly depends on what you think is real (though, to be fair, some suggest that what you think is real depends on what you think makes something true). However, it more often depends on what you think you justify as being true. That, however, has to do with straight up epistemology, and so must wait for another post.

Are We Living In A Computer Simulation?

We recently explored Cartesian skepticism, and its dark conclusion that we can’t know for sure that the external world exists. This post is in a similar vein, as it asks the question: Are we unknowingly living in a computer simulation? One difference between this dark idea and Descartes’ is that if we are indeed living in a computer simulation, there definitely would exist an external world of some sort — just not the one we think there is. Our simulators, after all, would have to live in some sort of an external world, in order for there to be computers upon which they could simulate us. But, of course, the world, on this scenario, that we think of as existing would be a mere virtual creation, and so, for us (poor unknowingly simulated beings) the depressing Cartesian conclusion would remain: our external world does not truly exist.

Of course, if you’ve been even a marginal part of contemporary culture over the last decade or two, you know the movie “The Matrix”, the premise of which is that most of humanity is living mentally in a computer simulation. (Physically, most of humanity is living in small, life-sustaining pods, in a post-apocalyptic real world of which they have no awareness.) You no doubt see the parallel between “The Matrix” and the topic of this post. (Other movies with similar premises include “Total Recall” and “Dark City”, and surely many more that I can’t think of off the top of my head. Which makes me think we have to do a philosophy-in-the-movies blog post soon…) But rest assured that this is no banal foray into Keanu Reevesean metaphysics. (“Whoa.”) The subject of existing in a computer simulation has been pored over to a dizzying extent by philosophers. There’s a lot of meat on this philosophical bone.

Nick Bostrom’s Simulation Argument

Nick Bostrom, a philosopher at Oxford, has developed a most interesting argument, the gist of which is to strongly suggest (with a high degree of probability) that we may indeed all be living in a computer simulation. His clever argument discusses advanced civilizations whose computational technology is so powerful that they can easily and cheaply run realistic simulations of their ancestors — people like you and me.

If these advanced civilizations are possible, then, says Bostrom, one of these three hypotheses must be true:

(1) Most (as in an overwhelmingly high statistical majority) civilizations that get to this advanced computational stage wind up going extinct. (The Doom Hypothesis)

(2) Most (as in an overwhelmingly high statistical majority) civilizations that get to this advanced computational stage see no compelling reason to run such ancestor simulations. (The Boredom Hypothesis)

(3) We are almost certainly living in a computer simulation. (The Simulation Hypothesis)

Bostrom claims that (1) and (2) are equally as likely as (3), but, really, it’s fairly straightforward to assume that they are both actually false. The Boredom Hypothesis, in particular, seems rather implausible. Though we don’t know what such an advanced civilization would think of as worth its time, it’s not unlikely that some significant fraction (at least) of advanced societies would run such easy and cheap simulations, either out of anthropological curiosity, or even for just entertainment purposes. (A lot of our best scientists surely play video games, right?) The Doom Hypothesis is slightly more plausible. Perhaps there’s a technological boundary that most civilizations cross that is inherently dangerous and destructive, and only a negligible fraction of civilizations make it over that hurdle. But it’s still tempting and not unreasonable to think that such a barrier isn’t inherent to social and scientific progress.

So, if civilizations don’t generally extinguish themselves before reaching computational nirvana, and if they don’t think that the idea of running ancestor simulations is a silly waste of time, then we have a clear path to the Simulation Hypothesis. Say that a thousand civilizations reach this computational stage and start running ancestor simulations. And say these simulations are so easy and inexpensive that each civilization runs a trillion simulations. That’s a quadrillion simulations overall. Now divide a quadrillion by however many civilizations there are in the universe, which is perhaps far less than a quadrillion, and you get the odds that you are living in a simulated civilization. Say, for the sake of argument, that there are a million civilizations in the universe. The odds are then a billion to one that you are living in a real civilization. The far more likely proposition is that you are living in a computer civilization.


One key assumption upon which this argument relies is that things like minds and the civilizations in which they reside are in fact simulatable. This is a contentious claim.

The theory that minds are able to be simulated is often labeled “functionalism” — it gets its traction from the idea that perhaps minds can emerge from hardware besides human brains. If we meet an alien from an advanced civilization, learn her language, and converse with her about the meaning of life, we’d like to say that she has a mind. But, if upon scanning her body, we discover that her brain is in fact made up of hydraulic parts, rather than our electro-chemical ones, would her different hardware mean that she isn’t possessed of a mind? Or would it be the case that, in fact, minds are the kinds of software that can run on different sorts of hardware?

If this is indeed the case, than minds can be classified as functional things — that is, a mental state (say, of pondering one’s own significance in an infinite cosmos) is not identical with any particular brain state, but is some sort of functional state that can be realized on all different sorts of hardware. And if this is true, then there’s no reason, in principle, that a computer couldn’t be one of those sorts of hardware.

Given our “successes” in the field of Artificial Intelligence (AI), I have long been skeptical of our ability to create minds in computers. And there’s a proud tradition in philosophy of this sort of skepticism — John Searle, for instance, is one of the more famous anti-AI philosophers out there. (You may have heard of his Chinese Room argument.) But, by and large, I think it is fair to say that most philosophers do come down on the side of functionalism as a philosophy of mind, and so Bostrom feels comfortable using it as a building block to his argument.

I can’t, in this post, get into the debate over AI, functionalism, and the mind, but I will pick on one interesting aspect of the whole simulation issue. Every time I think about successful computer simulations, my mind goes to the simulation of physics rather than the simulation of mental phenomena. Right now, I have a cat in my lap and my legs are propped up on my desk. The weight and warmth of my cat have very diverse effects on my body, and the extra weight is pushing uncomfortably on my knees. My right calf is resting with too much weight on the hard wood of my desk, creating an uncomfortable sensation of pressure that is approaching painful. My right wrist rests on the edge of my desk as I type, and I can feel the worn urethane beneath me, giving way, in spots, to bare pine. My cat’s fur fans out as his abdomen rises with his breathing — I can see thousands of hairs going this way and that, and I stretch out my left hand and feel each of them against my creviced palm. The fan of my computer is surprisingly loud tonight, and varies in pitch with no discernable rhythm. I flake off one more bit of urethane from my desk, and it lodges briefly in my thumb’s nail, creating a slight pressure between my nail and my flesh. I pull it out and hold it between my thumb and finger, feeling its random contours against my fingerprints.

At some point, you have to wonder if computing this sort of simulation would be just as expensive as recreating the scenario atom-for-atom. And maybe if a simulation is as expensive as a recreation, in fact the only reliable way to “simulate” an event would actually be to recreate it. In which case the idea of functionalism falls by the wayside — the medium now matters once again; i.e., feeling a wood chip in my fingernail is not something that can be instantiated in software, but something that relies on a particular sort of arrangement of atoms — wood against flesh.

Who knows, really? Perhaps future computer scientists will figure out all of these issues, and will indeed usher in an era of true AI. But until it becomes clearer that this is a reasonable goal, I’ll stick with my belief that I am not being simulated.

If I am being simulated, a quick aside to my simulator: Perhaps you don’t like meddling in the affairs of your minions, but I could really use a winning lottery ticket one of these days. Just sayin’…